Variational convergence and perturbed proximal method for saddle point problems

Recently D. Azé has introduced a variational metric between closed proper convex-concave functions. In the line of H. Attouch and R. Wets, a relationship between the metric-convergence and the Mosco-convergence is studied. It is also shown that the variational convergence theory enables us to explain the stability of some methods for finding saddle points. The method used here as a prototype is the proximal regularization method.